Optimal deterministic protocols for mobile robots on a grid

Abstract

A Multi Robot Grid System consists of m robots that operate in a set of n ≥ m work locations connected by aisles in a √n × √n grid. From time to time the robots need move along the aisles, in order to visit disjoint sets of locations. The movement of the robots must comply with the following constraints: (1) no two robots can collide at a grid node or traverse an edge at the same time; (2) a robot's sensory capability is limited to detecting the presence of another robot at a neighboring node. We present an efficient deterministic protocol that allows m=θ (n) robots to visit their target destinations in O (√dn) time, where each robot visits at most d ≤ n targets in any order. We also prove a lower bound that shows that our protocol is optimal. Prior to this paper, no optimal protocols were known for d > 1. For d=1 optimal protocols were known only for m=O (√n), while for m=O (n) only a randomized suboptimal protocol was known.

Part of this work was done while the authors were attending the Research Retreat on Sense of Direction and Compact Routing held in June 1997 at Certosa di Pontignano, Siena, Italy. This work was supported, in part, by CNR and MURST of Italy.